Description of quantum and classical dynamics via Feynman formulae

摘要

A method to describe classical and quantum evolution systems is presented. The method is based on the so-called Feynman formulae, i.e. on representations of solutions of evolution equations as limits of n-fold iterated integrals of some(usually elementary)functions when n tends to infinity. Such formulae are suitable for direct calculations and numeric modeling. On the other hand, these formulae are related to some functional(or path)integrals with respect to probability measures and Feynman type pseudomeasures. We outline some results related to classical and quantum systems on different geometrical structures.